This book gives an overview of paraconsistent logics - that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some (...) philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda (...) Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

Introduction -- The concept of logical consequence -- Tarski's characterization of the common concept of logical consequence -- The logical consequence relation has a modal element -- The logical consequence relation is formal -- The logical consequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in terms of their inferential properties -- Model-theoretic and deductive-theoretic (...) conceptions of logic -- Linguistic preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logical consequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logical consequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logical consequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system? (shrink)

Since the time of Aristotle, metaphysics has been an ill-defined term. This paper defines it as a logically idempotent metalinguistic identity of reality which couples the two initial ingredients of awareness: perceptual reality (the basis of physics), and cognitive-perceptual syntax, a formalization of mind. The explanation has been reduced to a few very simple, clearly explained mathematical ingredients. This paper contains no assumptions or arguable assertions, and is therefore presented as an advanced formulation of logic which has been updated (...) for meaningful reference to the structure of reality at large. This structure, called the Cognitive-Theoretic Model of the Universe or CTMU, resolves the problems attending Cartesian dualism by replacing dualism with the mathematical property of self-duality, meaning (for reality-theoretic purposes) the quantum-level invariance of identity under permutation of objective and spatiotemporal data types. The CTMU takes the form of a global coupling or superposition of mind and physical reality in a self-dual metaphysical identity M:L<-->U, which can be intrinsically developed into a logico-geometrically self-dual, ontologically self- contained language incorporating its own medium of existence and comprising its own model therein. (shrink)

Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF (...) INDUCTION. Introduction. Regularities and Projection. The Goodman Paradox. The Goodman Paradox, Regularity, and the Principle of the Uniformity of Nature. Summary. 5. MILL’S METHODS OF EXPERIMENTAL INQUIRY AND THE NATURE OF CAUSALITY. Introduction. Causality and Necessary and Sufficient Conditions. Mill’s Methods. The Direct Method of Agreement. The Inverse Method of Agreement. The Method of Difference. The Combined Methods. The Application of Mill’s Methods. Sufficient Conditions and Functional Relationships. Lawlike and Accidental Conditions. 6. THE PROBABILITY CALCULUS. Introduction. Probability, Arguments, Statements, and Properties. Disjunction and Negation Rules. Conjunction Rules and Conditional Probability. Expected Value of a Gamble. Bayes’ Theorem. Probability and Causality. 7. KINDS OF PROBABILITY. Introduction. Rational Degree of Belief. Utility. Ramsey. Relative Frequency. Chance. 8. PROBABILITY AND SCIENTIFIC INDUCTIVE LOGIC. Introduction. Hypothesis and Deduction. Quantity and Variety of Evidence. Total Evidence. Convergence to the Truth. ANSWERS TO SELECTED EXERCISES. INDEX. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal (...) language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure (...) with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

_The Logic of Our Language_ teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal (...) symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website. (shrink)

Homeostatic Property Cluster (HPC) theory suggests that species and other biological taxa consist of organisms that share certain similarities. HPC theory acknowledges the existence of Darwinian variation within biological taxa. The claim is that “homeostatic mechanisms” acting on the members of such taxa nonetheless ensure a significant cluster of similarities. The HPC theorist’s focus on individual similarities is inadequate to account for stable polymorphism within taxa, and fails properly to capture their historical nature. A better approach is to treat (...) distributions of traits in species populations as irreducible facts, explained in terms of selection pressures, genealogy, and other evolutionary factors. We call this view Population Structure Theory (PST). PST accommodates the view, implicit in biological systematics, that species are identified by reference to particular historical populations. (shrink)

Deductive Logic is designed as an intermediate-level text directed at upper-division students from philosophy and the humanities. Its focus is exclusively on deductive logic, avoiding altogether topics such as informal reasoning and scientific method normally included in introductory logic courses. Its exposition of logical topics is informal, with emphasis on explaining the basic concepts and procedures of modern symbolic logic in the simplest and most intuitive manner possible rather than on developing a rigorous formal system and (...) providing proofs of its properties. The fact that the text presupposes a course offered to philosophy students and serves to introduce them to logic as the "language of philosophy" has strongly influenced the selection of topics. The topics here are controversial, and the problems not easily resolved, but this text strives to relate the formal logical structures introduced to issues of philosophic interest. (shrink)

The study of biodiversity spans many disciplines and includes data pertaining to species distributions and abundances, genetic sequences, trait measurements, and ecological niches, complemented by information on collection and measurement protocols. A review of the current landscape of metadata standards and ontologies in biodiversity science suggests that existing standards such as the Darwin Core terminology are inadequate for describing biodiversity data in a semantically meaningful and computationally useful way. Existing ontologies, such as the Gene Ontology and others in the Open (...) Biological and Biomedical Ontologies (OBO) Foundry library, provide a semantic structure but lack many of the necessary terms to describe biodiversity data in all its dimensions. In this paper, we describe the motivation for and ongoing development of a new Biological Collections Ontology, the Environment Ontology, and the Population and Community Ontology. These ontologies share the aim of improving data aggregation and integration across the biodiversity domain and can be used to describe physical samples and sampling processes (for example, collection, extraction, and preservation techniques), as well as biodiversity observations that involve no physical sampling. Together they encompass studies of: 1) individual organisms, including voucher specimens from ecological studies and museum specimens, 2) bulk or environmental samples (e.g., gut contents, soil, water) that include DNA, other molecules, and potentially many organisms, especially microbes, and 3) survey-based ecological observations. We discuss how these ontologies can be applied to biodiversity use cases that span genetic, organismal, and ecosystem levels of organization. We argue that if adopted as a standard and rigorously applied and enriched by the biodiversity community, these ontologies would significantly reduce barriers to data discovery, integration, and exchange among biodiversity resources and researchers. (shrink)

This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on (...) it. The book is meant primarily for mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculus. Today we know of many calculi which have this property. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the (...) idea arises of a dual logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

Novel forms of matter, such as states made of gluons (glueballs), multiquark mesons or baryons and hybrid mesons are predicted by low energy QCD, for which several candidates have recently been identified. Searching for such exotic states of matter and studying their production and decay properties in detail has become a flourishing field at the experimental facilities now available or being built - e.g. BESIII in Beijing, BELLE II at SuperKEKB, GlueX at Jefferson Lab, PANDA at FAIR, J-PARC and in (...) the upgraded LHC experiments, in particular LHCb. A modern primer in the field is required so as to both revive and update the teaching of a new generation of researchers in the field of QCD. These lectures on hadron spectroscopy are intended for Master and PhD students and have been originally developed for a course delivered at the Stefan Meyer Institute of the Austrian Academy of Sciences. They are phenomenologically oriented and intended as complementary material for basic courses in particle and nuclear physics. The book describes the spectra of light and heavy mesons and baryons, and introduces the fundamental properties based on symmetries. Further, it derives multiplet structures, mixing angle, decay coupling constants, magnetic moments of baryons, and predictions for multiquark states and compares these with suitable experimental data. Basic methods of calculating decay angular distributions and determining masses and widths of resonances are also presented. The appendices provide students and newcomers to the field with the necessary background information, and include a set of problems and solutions. (shrink)

Those who speak of the philosophy of science do not all have the same sort of study in mind. For some it is speculation about the overall nature of the world. Others take it to be basic theory of knowledge and perception. And for still others, it is a branch of philosophical analysis focused speci is meant to be a study falling under fically on science. The present book this last category. Generally, such a study has two aspects: one, methodological, (...) dealing with the logical structure of science, the other, substantive, dealing with scientific concepts. Our concern here is primarily methodological; and, where discussion veers at times towards substantive matters, this will be largely for the purpose of illustrating underlying methodological points. It should also be added that our considerations will be of a general sort, intended to apply to all of science with no special concern for any particular divisions. Except in an incidental manner, therefore, we shall give no primary attention to special problems in the methodology of the social sciences or in the philosophy of physics or of biology. And if we draw the larger portion of our examples from the physical rather than from the behavioral sciences, this is done merely for simplicity, succinctness, and similar conveniences of exposition rather than out of specialized concern for any particular area. (shrink)

Deontic logic is a branch of logic that investigates normative concepts, systems of norms and normative reasoning. The formal languages of deontic logic include normative concepts that correspond to natural language notions such as ought, obligatory, permissible, forbidden and optional. The present book is an introduction to this branch of logic. Several basic deontic systems are described and some of their properties are explored. Every system is characterized both semantically using possible world semantics and axiomatically. (...) The final chapter includes soundness and completeness results for every system. The focus of the study is formal, but some philosophical questions are also raised, in particular: What is the meaning of the word "ought" and other normative notions as they occur in ordinary and philosophical discussions? Several distinctions between different kinds of obligations are considered, for instance the distinctions between prima facie and all things considered obligations and between conditional and unconditional obligations. The book is aimed at people with no prior knowledge of deontic logic but with some acquaintance with classical logic including some set theory. It should interest anyone who wants to know more about this area. (shrink)

Learn how to develop your reasoning skills and how to write well-reasoned proofs Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing (...) class='Hi'>terms and ideas, and provides a much-needed bridge to advanced work in mathematics as well as computer science. Original, inspiring, and designed for maximum comprehension, this remarkable book: Clearly explains how to write compound sentences in equivalent forms and use them in valid arguments Presents simple techniques on how to structure your thinking and writing to form well-reasoned proofs Reinforces these techniques through a survey of sets-the building blocks of mathematics Examines the fundamental types of relations, which is "where the action is" in mathematics Provides relevant examples and class-tested exercises designed to maximize the learning experience Includes a mind-building game/exercise space at www.wiley.com/products/subject/mathematics/. (shrink)

Robert B. Brandom is one of the most original philosophers of our day, whose book Making It Explicit covered and extended a vast range of topics in metaphysics, epistemology, and philosophy of language--the very core of analytic philosophy. This new work provides an approachable introduction to the complex system that Making It Explicit mapped out. A tour of the earlier book's large ideas and relevant details, Articulating Reasons offers an easy entry into two of the main themes of Brandom's (...) work: the idea that the semantic content of a sentence is determined by the norms governing inferences to and from it, and the idea that the distinctive function of logical vocabulary is to let us make our tacit inferential commitments explicit. Brandom's work, making the move from representationalism to inferentialism, constitutes a near-Copernican shift in the philosophy of language--and the most important single development in the field in recent decades. Articulating Reasons puts this accomplishment within reach of nonphilosophers who want to understand the state of the foundations of semantics. Table of Contents: Introduction 1. Semantic Inferentialism and Logical Expressivism 2. Action, Norms, and Practical Reasoning 3. Insights and Blindspots of Reliabilism 4. What Are Singular Terms, and Why Are There Any? 5. A Social Route from Reasoning to Representing 6. Objectivity and the Normative Fine Structure of Rationality Notes Index Displaying a sovereign command of the intricate discussion in the analytic philosophy of language, Brandom manages successfully to carry out a program within the philosophy of language that has already been sketched by others, without losing sight of the vision inspiring the enterprise in the important details of his investigation ' Using the tools of a complex theory of language, Brandom succeeds in describing convincingly the practices in which the reason and autonomy of subjects capable of speech and action are expressed. --J'rgen Habermas. (shrink)

One of the main aims of modern logic at its inception was to show that mathematics could be "reduced to logic"; that is, that mathematical notions could be defined in terms of logical constants in the sense in which we have defined some logical ...

Analytical philosophy of the last one hundred years has been heavily influenced by a doctrine to the effect that one can arrive at a correct ontology by paying attention to certain superficial (syntactic) features of first-order predicate logic as conceived by Frege and Russell. More specifically, it is a doctrine to the effect that the key to the ontological structure of reality is captured syntactically in the ‘Fa’ (or, in more sophisticated versions, in the ‘Rab’) of first-order (...) class='Hi'>logic, where ‘F’ stands for what is general in reality and ‘a’ for what is individual. Hence “f(a)ntology”. Because predicate logic has exactly two syntactically different kinds of referring expressions—‘F’, ‘G’, ‘R’, etc., and ‘a’, ‘b’, ‘c’, etc.—so reality must consist of exactly two correspondingly different kinds of entity: the general (properties, concepts) and the particular (things, objects), the relation between these two kinds of entity being revealed in the predicate-argument structure of atomic formulas in first-order logic. (shrink)

The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and (...) the logical constant ¬. A rule based account of the meanings of logical constants that appeals to the notion of incompatibility in the introduction rule for negation ensures the existence and uniqueness of the negation of every proposition. But it endows the negation operator with no more formal properties than those it has in minimal logic. (shrink)

Two new philosophical problems surrounding the gradation of certainty began to emerge in the 17th century and are still very much alive today. One is concerned with the evaluation of inductive reasoning, whether in science, jurisprudence, or elsewhere; the other with the interpretation of the mathematical calculus of change. This book, aimed at non-specialists, investigates both problems and the extent to which they are connected. Cohen demonstrates the diversity of logical structures that are available for judgements of probability, and explores (...) the rationale for their appropriateness in different contexts of application. Thus his study deals with the complexity of the underlying philosophical issues without simply cataloging alternative conceptions or espousing a particular "favorite" theory. (shrink)

The Process of Argument: An Introduction is a necessary companion for anyone seeking to engage in successful persuasion: To organize, construct, and communicate arguments. It is both comprehensive and accessible: An authoritative guide to logical thinking and effective communication. The book begins with techniques to improve reading comprehension, including guides on navigating through fake news and internet trolls. Then, readers are taught how to reconstruct deductive, inductive, and abductive presentations so that the logical structure is explicit. And finally, (...) there is a step-by-step guide for responding to these texts via the argumentative essay. Along the way are current examples from social media and elsewhere on the internet along with guides for assessing truth claims in an ever-complicated community worldview. Throughout, are carefully selected reading questions and exercises that will pace readers in order to ensure that the text is securely grasped and successfully applied. Key Features Offers guidance on how to read a text through self-analysis and social criticism Provides a step-by-step procedure for allowing the student to move from reading to reconstruction to being prepared to write an effective argumentative essay Presents truth theory and shows readers how they can helpfully acquaint themselves with a version of realistic, foundational epistemology Offers guidelines and helpful tools on how best to structure an argumentative, pro or con, essay Includes expansive coverage of inductive logic through the use and assessment of statistics Covers abductive logic as it applies to the analysis of narrative in argumentative writing Has up-to-date examples from the media, including from blogs, social media, and television Includes a helpful glossary of all important terms in the book. (shrink)

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

Phenomenology is the general study of the structure of experience, from thought and perception, to self-consciousness, bodily-awareness, and emotion. It is both a fundamental area of philosophy and a major methodological approach within the human sciences. Experiencing Phenomenology is an outstanding introduction to phenomenology. Approaching fundamental phenomenological questions from a critical, systematic perspective whilst paying careful attention to classic phenomenological texts, the book possesses a clarity and breadth that will be welcomed by students coming to the subject for (...) the first time. Accessibly written, each chapter relates classic phenomenological discussions to contemporary issues and debates in philosophy. The following key topics are introduced and explained: the methodological foundations of phenomenology intentionality as the ‘mark of the mental’ and the problem of non-existent objects perceptual experience, including our awareness of things, properties, and events the experience of body, self, and others imaginative and emotional experience detailed discussions of classical phenomenological texts, including: Brentano's _Psychology from an Empirical Standpoint _ Husserl's _Logical Investigations_, _Cartesian Meditations, _and On_ the Phenomenology of the Consciousness of Internal Time _ Heidegger’s _History of The Concept of Time,_ and _Being and Time _ Stein's _On the Problem of Empathy _ Sartre's _Transcendence of the Ego_, _Sketch for a Theory of the Emotions,_ and _The Imaginary _ Merleau-Ponty's Phenomenology of Perception. Also included is a glossary of key terms and suggestions for further reading, making this book an ideal starting point for anyone new to the study of phenomenology, not only in Philosophy but related disciplines such as Psychology and Sociology. (shrink)

The subtitle of this text intended for philosophy students’ 2nd course in logic is in no way misleading. It is a lucid introduction to the philosophic activities of uncovering metaphysical presuppositions of logical techniques and altering logical techniques, and hence assessments of deductive validity, to conform to metaphysical presuppositions. They do not, though, assume that techniques for assessing deductive validity are or should be wholly dependent upon metaphysical presuppositions. They write on p. 213 in their section on intensional (...) discourse: "And logic wherever possible ought not to wait upon philosophy, for logic wherever possible ought to be neutral between different philosophical analyses." In their investigations of metaphysical presuppositions and logical techniques, they consider primarily the consequences of existential presuppositions about the use of singular terms, viz., individual variables, individual names, and definite descriptions. They favor freeing use of singular terms from existential presuppositions. The consideration of allowing non-referring names and definite descriptions makes their text one of the first, if not the first, for teaching Free Logic. The gist of Free Logic is not to allow existential generalization of Fb to unless there is an auxiliary premise asserting the existence of b, because use of the name b has been freed from the presupposition that it names something. It is suitable that these authors have a text on Free Logic since Lambert is the major figure in its origin while van Fraassen has established some of the most significant results about Free Logic systems. They go on to consider alternative logical rules to those of Russell for dealing with nonreferring definite descriptions. These alternatives to standard logic are philosophically motivated. They are not simply dumped upon students as rules for symbol manipulation. For instance, on pp. 152-157 they give a succinct analysis of the Russell-Meinong debate when they agree with Meinong that one can talk of the thing that is such and such without accepting that there is such a thing. The treatment of singular terms leads them to discussions of topics such as: What is it for a logic to be extensional and is Free Logic extensional?, the substitution interpretation of quantifiers, and the notion of presupposition. (shrink)

In this thesis I investigate the notion of experience in German Idealist Philosophy. I focus on the exploration of an alternative to the transcendental model notion of experience through Schelling's insight into the notion of logogrif. The structural division of this project into two sections reflects the two theoretical standpoints of this project, namely the logic and the logogrif of experience. The first section - the logic of experience - explores the notion of experience provided in Kant's Critique (...) of Pure Reason, Critique of Judgement and Fichte's Science of Knowledge. I argue that Kant's fundamental question about the possibility of synthetic a priori judgements succeeds in thematising the aporia of cognitive experience but results in a subject-oriented, representational model which radically confines the notion of experience to the constitutive laws of the understanding or to the normative precepts of Reason. Experience is founded upon a sharp division between faith and knowledge, will and logic, desire and reflection, absolute and finitude. Fichte's endeavour to articulate a non-representational account of experience, does not succeed in extricating itself from the representational model, so long as experience is reduced to the ever-producing deeds of the self-positing ego. Despite the serious differences between Kant's and Fichte's notions of experience, both accounts, so long as they unfold from a transcendental standpoint, attempt to resolve experience into conceptual laws or determinations of the ego's absolute will. Experience is transformed into an object of the subject's cognitive or volitional faculties. The paradoxes of man's interaction with the world are intended to be accommodated either by the law-giving spontaneity of the understanding and the Architectonic of Pure Reason or by the overpowerful primordial act of the self-positing ego. This implies the conceptualisation of the self in terms of constant identity-through-time, or sheer self-determination. However, this conceptualisation remains at the normative or prescriptive level, which in turn is projected upon the world. The latter, though appears as the subject's property, essentially remains alien and opaque, confirming the radical limitations of the ego rather than its order-giving authority. Moreover, this notion of experience is ultimately founded upon a radical expulsion of the divine from the world, the de-spiritualisation of the sensual and the de-sensualisation of the spiritual, the sharp juxtaposition between absolute and finitude. This results in a self-defeating subjectivity, whose firm identity and rule-giving authority does not rescue it from its perennial unattainability to 'organise the conditioned' or 'conquer the unconditioned'. In Kant's and Fichte's thought, however, I detect elements that potentially transgress their transcendental account of experience. These are found in Kant's concept of spontaneity and free play between understanding and imagination, and Fichte's concept of productivity. I argue that these elements lose their potential dynamism, so long as they are absorbed by the transcendental demands for the solution of the aporias of logic. However, these elements point to the need for a radical re-conceptualisation of the notion of experience. This is provided by means of Schelling's logogriflic approach, which constitutes the theme of the second section. The second section - the logogrif of experience - attempts to articulate a different approach towards the notion of experience, through an exploration of Schelling's versatile and provocative thought. This section focuses on Schelling's original insight into the notion and act of logogrif, which opens the dialogue between logos and mythos, cosmic becoming and human soul, cosmic imagination and human reflection, faith and knowledge. This section attempts to illuminate Schelling's fascinating philosophical investigations and discoveries that have been rather overlooked, possibly, due to Hegel's overwhelming critique. This section, after a brief critical examination of the Identity Philosophy, attempts to elucidate Schelling's notion of experience through his middle works, Of Human Freedom, Ages of the World, The Deities of Samothrace, which are treated as a self-developing trilogy. Schelling re-addresses the aporias of logic not as part of Reason's self-interrogation but as part of the cosmic paradoxes and living experiences. In this way, Schelling resets the scene of the debate on the conditions of possibility for cognitive experience by putting on the stage the enigmas of the cosmos and life rather than the Tribunal of Reason. Logic itself is conceived as a potency in the cosmic becoming, and consequently can no longer attempt to establish the transcendental conditions for the possibility of cognitive experience. Cosmic becoming, in which man is an active part, is conceived as the process of the movement, the interaction, the transformations and transmutations of multiple potencies. These, far beyond any mechanical conceptualisation, appear as self-moving and yet interdependent, unknown yet familiar, inscrutable and yet manifest powers, describing the mystery of life itself. The latter is depicted as an ever-recurrent act of longing for self-expression as active unity. Experience is conceived as the lived process of a network of living potencies, which may not only resist rational powers but may also puzzle and seize them. In this context, reflection acquires a plastic dimension, as opposed to its rigidity in the representational model of experience. Reflection depicts cosmic longing's self-formation, whose man is part. This self-bending formation partially illuminates the nature of longing, and from this standpoint is the logic of the longing. However, this formation is movable, transmutable and mostly ineffable, and from this standpoint is the logic of a riddle: a logogrif. Logogrif is the transitive term that attempts to describe the transition of experience from its enacted phase to its allusive conceptual utterance, and in this sense the term itself participates in both phases, as both form of thought and form of life. The logogrific approach to experience in turn transposes us as from the realm of pure concepts to the realm of the mystery of life, from pure thought to acts of longing, from the Architectonic of Pure Reason to Cosmic Theurgy. The latter term attempts to grasp the paradox and dynamism of cosmic and non-cosmic becoming by means of multiple, vanishing and ever-recurring, transmutable potencies, or in Schelling's terms 'the magic of insoluble life'. Schelling's logogrific account consists in a powerful voice for the re-enchantment of the world, the introduction into the notion of experience of the imminence of the divine. This is not suggested in terms of the adoption of old religious doctrines but by means of the discovery and re-discovery of the theurgy of life, through the intensification of our artistic mood, the creative expansion of our deeds. This notion of experience allows for the reconsideration of the notion of the self, in terms of a dynamic, conflictual process between conscious and unconscious powers and the critical revaluation of the accounts of subjectivity which reduce it to the sphere of self-consciousness. The thesis concludes with the need for an investigation into the relation between logos and mythos, which only tangentially has been introduced by the present project. In this context it will be possible to re-appraise the potential that the logogrific approach opens for an alternative to both logical and traditional mythological patterns of thinking. (shrink)

Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working (...) with semantic generalizations – are addressed. Finally, I’ll introduce the case studies that I’ll be dealing with in part II. Chapter 2 is concerned with the origins and development of Jaśkowski’s discussive logic. The main idea of this chapter is to systematize the various stages of the development of discussive logic related researches from two different angles, i.e., its connections to modal logics and its proof theory, by highlighting virtues and vices. Chapter 3 focuses on the Gentzen-style proof theory of discussive logic, by providing a characterization of it in terms of labelled sequent calculi. Chapter 4 deals with the Gentzen-style proof theory of relevant logics, again by employing the methodology of labelled sequent calculi. This time, instead of working with a single logic, I’ll deal with a whole family of them. More precisely, I’ll study in terms of proof systems those relevant logics that can be characterised, at the semantic level, by reduced Routley-Meyer models, i.e., relational structures with a ternary relation between states and a unique base element. Chapter 5 investigates the proof theory of a modal expansion of intuitionistic propositional logic obtained by adding an ‘actuality’ operator to the connectives. This logic was introduced also using Gentzen sequents. Unfortunately, the original proof system is not cut-free. This chapter shows how to solve this problem by moving to hypersequents. Chapter 6 concludes the investigations and discusses the future of the research presented throughout the dissertation. (shrink)

The Logic & Structure project is about the language of mathematical logic and how it can be of use in the visual arts. It involves a conversation between a mathematical logician and a group of artists. The project is ongoing, and this is a report on its first two phases. This text has two parts. The first, “Logic”, is a short introduction to certain aspects of logic, as it was presented to the participants. The (...) second part, “Structures”, describes some of the outcomes.The inspiration for the project comes from modern model theory whose advances revealed the extent to which formal methods may be helpful in describing and analysing mathematical structures. While the structures that are studied are often immensely complex, the formal language in which their properties can be expressed is simple. Its syntax is precisely defined and well understood, and this understanding often successfully guides us in our explorations of the rich world of mathematical objects. Our goal is to see the extent to which a similar approach could be of value when talking about works of art as structures. To this end, one could try to describe existing art objects in terms of suitably chosen formal languages, but we follow a reverse route. The language is described first, and the participating artists are asked to come up with artwork in which formal elements and their relations are chosen in advance, making it easier to identify those features of the created pieces that can be formally expressed. In other words, we are not thinking of applying formal methods to create art; rather we want to begin with samples that can serve as material for discussion. (shrink)

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the (...) uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book accessible as well as invaluable. (shrink)

One of his six introductions to philosophy, widely used by students in Alexandria, Ammonius' lecture on Porphyry was recorded in writing by his students in the commentary translated here. Along with five other types of introductions (three of which are translated in the Ancient Commentators on Aristotle volume Elias and David: Introductions to Philosophy with Olympiodorus: Introduction to Logic) it made Greek philosophy more accessible to other cultures. These introductions became standard in Ammonius' school and included a popular (...) set of five or more definitions of philosophy, some of them drawn from commentaries on quite different works. Ammonius' lecture expounded the most celebrated and discussed previous introduction written by Porphyry 200 years earlier, which was devoted to five main technical terms of Aristotle's logic. Ammonius was sympathetic to Porphyry because they both sought to harmonise the views of Plato and Aristotle with each other, arguing in different ways that the two philosophers did not disagree about the nature of universals. Porphyry's introduction was a hugely influential work for centuries after its composition, and this commentary by Ammonius served to maintain its position at the centre of later schools of philosophy. This English translation of Ammonius' work is the latest volume in the Ancient Commentators on Aristotle series and makes this philosophical work accessible to a modern readership. The translation is accompanied by an introduction, comprehensive commentary notes, bibliography, glossary of translated terms and a subject index. (shrink)

Professor Little presents an introduction to the philosophy of social science with an emphasis on the central forms of explanation in social science: rational-intentional, causal, functional, structural, materialist, statistical and interpretive. The book is very strong on recent developments, particularly in its treatment of rational choice theory, microfoundations for social explanation, the idea of supervenience, functionalism, and current discussions of relativism.Of special interest is Professor Little’s insight that, like the philosophy of natural science, the philosophy of social science can (...) profit from examining actual scientific examples. Throughout the book, philosophical theory is integrated with recent empirical work on both agrarian and industrial society drawn from political science, sociology, geography, anthropology, and economics.Clearly written and well structured, this text provides the logical and conceptual tools necessary for dealing with the debates at the cutting edge of contemporary philosophy of social science. It will prove indispensible for philosophers, social scientists and their students. (shrink)

György Márkus, as a leading member of the Budapest School led by György Lukács in Hungary, is closely concerned with aesthetics. His final unfinished writings in political exile in Sydney were focused on the question of modern cultural autonomy. From the 1960s to the new century, from Budapest to Sydney in Australia, he established a new form of Neo-Marxist aesthetics on the basis of critical theory drawn from Lukács to the Frankfurt School. His aesthetics includes three dimensions: an aesthetics of (...) praxis, a reconstruction of Lukács’s aesthetics and a theory of aesthetic modernity. His aesthetics is characteristic of analytic philosophy, especially ‘categorical analysis’. It shifts from philosophical aesthetics in the Hungarian period, which is based on an ontological foundation, that is, materialist phenomenology, to social or sociological aesthetics in the Australian period concerning social modernity, institution, constitution, culture, and so on. This is a turn from a philosophical paradigm to a structural one as regards aesthetics, which indicates a break with Lukács’s late return in the early 1960s to Hegelian inspired Ontology of Social Being. Márkus is strictly and essentially an essayist in fragments, who distinguishes himself from the other members of the Budapest School in this way. Ironically, this genre is once again influenced by the young Lukács’s aesthetics. (shrink)

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. We also assurne (...) a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model oflogic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based-rather, any conclusions to be drawn about the foundations of mathematics co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory. (shrink)

The early calculus is a popular example of an inconsistent but fruitful scientific theory. This paper is concerned with the formalisation of reasoning processes based on this inconsistent theory. First it is shown how a formal reconstruction in terms of a sub-classical negation leads to triviality. This is followed by the evaluation of the chunk and permeate mechanism proposed by Brown and Priest in, 379–388, 2004) to obtain a non-trivial formalisation of the early infinitesimal calculus. Different shortcomings of (...) this application of C&P as an explication of inconsistency tolerant reasoning are pointed out, both conceptual and technical. To remedy these shortcomings, an adaptive logic is proposed that allows for conditional permeations of formulas under the assumption of consistency preservation. First the adaptive logic is defined and explained and thereafter it is demonstrated how this adaptive logic remedies the defects C&P suffered from. (shrink)

A philosopher who has mastered the standard two-valued propositional calculus and who is curious to find out what the systems of many-valued logic, strict implication and modal logic are all about, should reach for this small booklet from the series Monographs in Modern Logic It explains in a compact but remarkably lucid way the rationale of these non-standard logics and gives access to the literature of the field. There are numerous references to a selected bibliography, the most (...) recent titles of which are from 1965. But the reader is not only informed about the technical properties of these systems, he is also given a sound perspective in which to see their intuitive significance. It is characteristic that the author distinguishes on the very first page between a logic and a calculus associated with a logic. (shrink)

This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of λ-abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than (...) other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher Order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher order languages Offers an abundance of: - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context. (shrink)

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic, natural deduction and the normalization theorems, the sequent calculus, including cut-elimination and mid-sequent theorems, and various (...) applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics. (shrink)

How does science work? Does it tell us what the world is "really" like? What makes it different from other ways of understanding the universe? In Theory and Reality , Peter Godfrey-Smith addresses these questions by taking the reader on a grand tour of one hundred years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory (...) and Reality covers logical positivism the problems of induction and confirmation Karl Popper's theory of science Thomas Kuhn and "scientific revolutions" the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student a glossary of terms explains key concepts and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years. Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Guibert of Tournai's Letter to Lady Isabelle:An Introduction and English TranslationLarry F. Field, Jacques Dalarun, Sean L. Field, and Guibert of TournaiIntroductionGuibert, from the noble family of As-Piès, was born near Tournai around 1200. From his hometown he traveled to Paris for his art degree, and completed the curriculum in theology there before entering the Franciscan Order around 1240. He may have participated in Louis IX's crusade of (...) 1248, but, if so, was surely back in Paris by 1254 at the latest, since he preached a cycle of sermons de dominicis et de sanctis to the university community before summer 1255.1 His regency as Franciscan master of theology at Paris was probably around 1259–1261,2 about the time he [End Page 31] completed his Eruditio regum et principum for Louis IX,3 and began his most substantial work, the Erudimentum doctrinae.4 Other significant treatises include his De pace et animi tranquillitate (ca. 1275)5 written for Marie de Dampierre, and the Collectio de scandalis ecclesiae, prepared for the Second Council of Lyon.6 Guibert died in Tournai on 7 October 1284.7Sometime around 1254, Guibert wrote a long letter of spiritual advice to Isabelle (1225–70), the sister of King Louis IX.8 Isabelle was herself a remarkable figure. She had rejected several proposals of marriage, including that with Conrad, the heir to Emperor Frederick II, in 1243, in spite of pressure from her family and Pope Innocent IV. But following a bout of serious illness at about that time,9 her family accepted her [End Page 32] decision to remain unwed. There is no evidence, however, that Isabelle ever pronounced a formal vow of virginity. Through the 1250s she simply remained at the Capetian court as a virgin princess with an increasing reputation for piety and indeed holiness, praised in lavish terms by Innocent IV in 1253 and Alexander IV in 1256.10 This piety took a distinctly Franciscan turn by 1254, when Pope Innocent IV granted her request for Franciscan confessors,11 which would ultimately result in her foundation of Longchamp, a house of Sorores minores just west of Paris, by 1260.12 Guibert's letter shows no awareness of such a project, indicating that it must have been written before spring 1255, by which time the land for Longchamp was being purchased on Isabelle's behalf.13 Guibert thus wrote at the moment when Isabelle was forming her first ties to the Franciscans, but well before her move to Longchamp, where she lived out the 1260s as resident lay patron (but never a nun).Guibert's Letter is really a short treatise of spiritual and moral advice, tailored to a celibate princess. It is organized around Psalm 44:14–15, All the glory of the king's daughter is within in golden fringes, clothed around with varieties. In a five-part structure, the king's daughter stands for a heavenly inheritance; glory within represents internal purity; gold indicates virginity; the fringes are a sign of humility; and clothed around with varieties points to honest comportment. The resulting "royal garment," however, is rather unequally woven together, with section one on the "heavenly inheritance" and the intertwined sections three and four on virginity and humility receiving by far the most space. In fact, section one forms a sort of treatise-within-a-treatise, organized as a ten-step ascent to the heavenly inheritance awaiting the daughter of the king. [End Page 33]The Letter to Lady Isabelle was first edited by Alphonse de Poorter in 1931, from a manuscript which contained only part of the text.14 The full text was brought into print by Sean Field in 2003,15 and translated into French by Jacques Dalarun in 2014.16 Yet in spite of these advances, the Letter has remained little noticed by scholars. Anne-Hélène Allirot offered several perceptive pages in 2010, stressing the way Guibert's treatment of hereditas implies that female members of the royal family might be particularly able to embody Capetian claims to holiness.17 That same year, in the only recent article dedicated specifically to this Letter, Rina Lahav... (shrink)

The word 'philosophy' as well as the conjuring expression 'Indian philosophy' has meant different things to different people-endeavours and activities, old and new, grave and frivolous, edifying and banal, esoteric and exoteric. In this book, the author has chosen deliberately a very dominant trend of the classical (Sanskrit) philosophical literature as his subject of study. The age of the material used here demands both philological scholarship and philosophical amplification. Classical pramanasastras usually deal with the theory of knowledge, the nature of (...) inference and language, and the related questions of ontology and semantics. Several important concepts and theories have been singled out for critical analysis and clarification in modern terms so that the results may be intelligible to modern students of both Sanskrit and philosophy. It is hoped that such an attempt will kindle the enthusiasm of young scholars in the field and inspire them to proceed in this comparatively new area of research and explore further and more interesting possibilities. (shrink)

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights (...) from Aristotle's syllogistic, Scholastic logicians, Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

When we hear the term "Japanese philosophy" we think of Zen Buddhism or the Shinto scriptures. Yet one of the great 20th century interpreters of Western philosophy, Nishida Kitaro, lived and wrote in the Japanese islands all his life, laboring at an ultimate synthesis of oriental thought and Western hermeneutics. To be sure, Nishida's aim was to understand his own cultural influences in relation to the Western world. What distinguished him, however, was his passion for rendering oriental metaphysics understandable in (...) the language of Western philosophy, and his attempts to contrast the paradoxicality of Buddhist logic with the logical strategies of Aristotle, Kant, or Hegel. Featured in this book is an interpretation of Nishida's writings. Professor Carter focuses on the Japanese thinker's notion of "basho," a concept of nothingness as field, place or topos as borrowed from Plato's Tim'us. Expounding on the logical foundations and archaic elements in Nishida's work, and carefully explaining Nishida's critical approach to the questions of God, religion and morality, and pure existence, this discerning book offers students of Western philosophy and oriental thought alike a highly readable introduction to the teachings of a true world philosopher. (shrink)

A comprehensive yet concise introduction to central topics, debates, and techniques of moral philosophy in the analytic tradition, this volume combines a thematic, issue-oriented format with rigorous standards of clarity and precision. Thomas introduces fundamental concepts and terms, proceeding through a step-by-step exploration of five general areas of debate: the specification of moral judgment; moral judgment and the moral standard; the justification of moral judgment; logic, reasoning, and moral judgment; and moral judgment and moral responsibility. Key historical (...) and contemporary figures in moral philosophy, including Plato, Aristotle, Kant, Hume, Mill, Hare, Ross, Nagel, Foot, Stevenson, and Dancy, are used effectively as a means of examining the topics themselves. (shrink)

In this paper, I discuss the general features of what I call ‘the semantics of message and attachment’. According to this theory, utterances of declarative sentences may be semantically associated with a plurality of information contents. I explain how this suggestion may provide a promising tool for the analysis of a variety of phenomena in the semantics for natural languages, such as complex demonstratives, dangling adverbs, or appositive clauses. I then focus on certain structural aspects of the theory, in particular (...) pertaining to the demands it imposes on the lexicon, and on the role it plays with respect to the truth-conditions for an utterance. In this last respect, I also discuss the logical outcomes of the theory, and I compare what I call a ‘content-containment’ approach to validity with a more traditional, truth-conditional understanding. (shrink)

This book guides readers by gradual steps through the central concepts and debates in the philosophy of science. Using concrete examples from the history of science, Kent W. Staley shows how seemingly abstract philosophical issues are relevant to important aspects of scientific practice. Structured in two parts, the book first tackles the central concepts of the philosophy of science, such as the problem of induction, falsificationism, and underdetermination, and important figures and movements, such as the logical empiricists, Thomas Kuhn, and (...) Paul Feyerabend. The second part turns to contemporary debates in the philosophy of science, such as scientific realism, explanation, the role of values in science, the different views of scientific inference, and probability. This broad yet detailed overview will give readers a strong grounding whilst also providing opportunities for further exploration. It will be of particular interest to students of philosophy, the philosophy of science, and science. (shrink)